It is well known ([1]}, [2]}, [3]}) that
\(b_{0}+\frac{a_{1}}{b_{1}}\genfrac{}{}{0.0pt}{}{{}}{+}\frac{a_{2}}{b_{2}}\genfrac{}{}{0.0pt}{}{{}}{+\cdots +}\frac{a_{n}}{b_{n}}=\frac{p_{n}}{q_{n}}\qquad \left( n\ge 1\right) ,\) 
